Let $\mathbf{A}$ and $\mathbf{B}$ be De Morgan monoids. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism:
$h(x \vee y)=h(x) \vee h(y)$, $h(x \cdot y)=h(x) \cdot h(y)$, $h(x')=h(x)'$ and $h(1)=1$.